The core and the bargaining set for multi-choice games

Abstract

Multi-choice games provide a mathematic model for the complex interactions among the rational agents which have several activity levels, based on the fuzzy set theory. For obtaining the stable payoff vectors, this paper extends the core, the dominance core and the bargaining set to the multi-choice games with coalition structure. And then we prove that the core is a subset of the dominance core, that both the core and the dominance core are two subsets of the bargaining set, and that the bargaining set is existent.